If an object of dimension 40cm×30cm×10cm is floating on a liquid of density 1g/cc.What height of the object will be exposed outside of the water given that the density of object is 0.92g/cc?
Volume of object = 40*30*10=12000 cm³
Principle of floatation says that the mass of liquid displaced by a floating object equals the mass of the object. (C.F. Archimedes)
For a density of 0.92 g/cc floating on a liquid of density 1.0 g/cc, the mass of liquid displaced is 0.92*12000=11040 g ≡ 11040 cc.
Therefore the volume of object exposed is 12000-11040=950.
The height of object exposed depends on the face completely immersed.
If the 40*30 cm^2 face is immersed, then the height of object exposed is 950/(40*30)=0.792 cm.
For other immersed faces, the height can be calculated similarly.
How is the density of an object determined?(1 point)
Responses
by dividing the mass of an object by its volume
by dividing the mass of an object by its volume
by multiplying the volume of an object by its mass
by multiplying the volume of an object by its mass
by subtracting the mass of an object from its volume
by subtracting the mass of an object from its volume
by adding the volume of an object to its mass
To determine the height of the object that will be exposed outside of the water, we need to compare the densities of the object and the liquid. Here's how you can do it:
Step 1: Calculate the volume of the object.
The volume of the object can be calculated using the formula:
Volume = length × width × height
Given:
Length = 40 cm
Width = 30 cm
Height = 10 cm
Volume = 40 cm × 30 cm × 10 cm
Volume = 12,000 cm³
Step 2: Calculate the mass of the object.
The formula to calculate the mass is:
Mass = Volume × Density
Given:
Density of the object = 0.92 g/cc
Volume = 12,000 cm³
Mass = 12,000 cm³ × 0.92 g/cc
Mass = 11,040 grams (or 11.04 kg)
Step 3: Determine the buoyant force.
The buoyant force is the force exerted by the liquid on the object when it is submerged.
Buoyant force = Volume of the object × Density of the liquid × g (acceleration due to gravity)
Given:
Density of the liquid = 1 g/cc
g = 9.8 m/s² (standard acceleration due to gravity)
Buoyant force = 12,000 cm³ × 1 g/cc × 9.8 m/s²
Buoyant force = 117,600 N
Step 4: Calculate the submerged height of the object.
The submerged height of the object can be calculated using the formula:
Submerged height = Buoyant force / (Area × Density of the liquid × g)
Given:
Area = length × width
Submerged height = 117,600 N / (40 cm × 30 cm × 1 g/cc × 9.8 m/s²)
Submerged height = 100 cm
Therefore, the height of the object that will be exposed outside of the water is:
Height of the object - Submerged height
10 cm - 100 cm = -90 cm
Since we obtain a negative value, it means that the object will be fully submerged in the water.